The metallic conductor of each electrode in the battery.in this model which are actually the two 'plates' of the 'battery-Earth' capacitor system ?
In practice (if 'in practice' makes any sense in this scenario with virtually zero actual capacitance), assuming the battery case is metallic which it probably is, there will be a capacitance between the outer case of the battery and Earth (the two 'plates') then you will effectively have two further capacitors in parallel (but in series with the case-Earth 'capacitance') to the battery electrodes
An ideal voltmeter has infinite resistance. But it is impossible for a real world voltmeter to have infinite resistance. They usually come with 1 MOhm or 10MOhm internal resistance, so that'll be your 'R'.Not sure to understand the model: how is the voltmeter connected here ? Are you considering a simple 'RC' series circuit ?
[In fact, I often measure kV/ua stuff with cheap multimeters (they tend to blow up on a regular basis, no point buying expensive ones) and I don't bother with the current selections, I just pass the current straight through the 'voltmeter' setting, giving me ua = volts based on a 1 MOhm internal resistance.]
FWIW There is no such thing as an infinite resistance. It's funny really, because intuitively you'd expect 'something' to be a perfect insulator and 'nothing' to be a perfect conductor, but reality treats us to something non-intuitive that there is no such thing as a perfect insulator, but there is such a thing as a perfect conductor! Your voltmeter will always pull the battery terminal to ground when you try to measure it, there is nothing connected to the other terminal to stop that. A capacitance would slow that down, but not stop it.